Who would be authorized to administer drugs on the way to a hospital? An EMT or a Paramedic? I'm writing a tv pilot in which a girl survives a car accident but has a subdural hematoma, and one of the first responders is the one who caused the crash, so he injects her with a blood thinner to try to kill her before he's revealed.
In NJ, only a paramedic can administer drugs in that setting. That said, the way we do things in northern NJ, one medic rides in the back of the ambulance, where he/she treats the patient, and at least one EMT would be in the back also and might hold onto things at the medic's request. If a medic knows and trusts an EMT well enough, he or she might allow the EMT to make minor adjustments to the rate of flow on a saline drip, but that's unlikely to play a role in the situation you're conveying.
If your story has a very experienced EMT -- perhaps one who's in the midst of taking a paramedic course or even training to become an RN or doctor -- who chooses to administer a drug in an attempted murder, it would be very difficult for that to go unnoticed by the paramedic Ambulances are cramped spaces in the best of situations. It could be done, I suppose, but you'd have to have a very opportunistic EMT who takes advantage of a split-second opportunity.